This problem models pollution effects in the great lakes. we assume pollutants are flowing into a lake at a constant rate of i kg/year, and that water is flowing out at a constant rate of f km3/year. we also assume that the pollutants are uniformly distributed throughout the lake. if c(t) denotes the concentration (in kg/km3) of pollutants at time t (in years), then c(t) satisfies the differential equationdcdt = − fv c + ivwhere v is the volume of the lake (in km3). we assume that (pollutant-free) rain and streams flowing into the lake keep the volume of water in the lake constant.

(a) suppose that the concentration at time t = 0 is c0. determine the concentration at any time t by solving the differential equation. c(t) = (to enter c0 in your answer, type "c_0", that is, "capital c, underscore, zero")
(b) find lim t→[infinity] c(t) = incorrect: your answer is incorrect.
(c) for lake erie, v = 458 km3 and f = 175 km3/year. suppose that one day its pollutant concentration is c0 and that all incoming pollution suddenly stopped (so i = 0). determine the number of years it would then take for pollution levels to drop to c0/10. give your answer in decimal form, rounded to the nearest year. years

(d) for lake superior, v = 12221 km3 and f = 65.2 km3/year. answer the same question as in part (c) for lake superior. years